Motion of small solid particles in a viscous fluid enclosed in a cavity

The motion of a solid particle embedded in a viscous fluid in a closed container requires a precise account of wall effects when in creeping flow. The boundary integral method, which amounts to solving a Fredholm integral equation for the stress on the particle and walls, is used here. The accuracy of the method is improved by using curvilinear six-node triangular boundary elements, the size of which is specially adapted to the particle shape and position with respect to walls. The method is applied to resolve the case of a moving particle in a parallelepiped container. It is validated by comparing with earlier analytical results for a sphere interacting with two parallel or perpendicular walls and with numerical results for a sphere in the center of a cubic container. Results are then provided for a spherical and an ellipsoidal particle, both either with imposed motion or settling in a cubic container.